• Watchful Hags, *Snakes of Grace* (1996)

• Jupiter Pore, *Gneumos* (1980)

• Sixmith, *Internecine* (2010)

• The Hext, *Celestial Chimes* (1982)

• Why We Wander, *W3* E.P. (1986)

• Zoön, *Zoönotic Rhythms* (2011)

• Fen Witches, *Wild Hunt* (1998)

• Virolator, *V-003* (2014)

• Slow Exploding Gulls, *Yr Wylan Ddu* (2003)

• Doris Day, *The Best Of…* (1987)

• Sirium, *MoCoT* (2013)

Previously pre-posted:

• Toxic Turntable #1

• Toxic Turntable #2

• Toxic Turntable #3

• Toxic Turntable #4

• Toxic Turntable #5

• Toxic Turntable #6

• Toxic Turntable #7

• Toxic Turntable #8

• Toxic Turntable #9

• Toxic Turntable #10

Filed under: Currently Listening..., Music Tagged: albums, avant garde music, avant-folk, contemporary music, Currently Listening..., electronic, electronic music, experimental music, Fen Witches, folk, folk music, indie, Jupiter Pore, music, neo-folk, playlist, post-folk, rock, Sirium, Sixmith, The Hext, Virolater, Watchful Hags, Why We Wander, Zoön ]]>

You can then ban or un-ban the choice of vertex-jump as you can ban or un-ban direct choices of vertex. These two methods of random choice are effectively the same, but one can be simpler to program than the other. That’s why I’ve come across some new fractals by using vertex-jumps. Here they are:

vertices = 4, vertex-jump = (1,2,3,4), ban on same choice twice in a row

vertices = 4, vertex-jump = (1,2,3,4), ban on 2 in row (black-and-white version)

*v* = 4, *vj* = (1,2,3,4), ban on choice *c* + 2 from previous choice *c*

*v* = 4, *vj* = (1,2,3,4), ban *c* + 2 (animated gif)

*vj* = (1,2,3,4), ban *c* + 2 (black-and-white)

*vj* = (1,2,3,4), ban *c* + 0 at time *t+1* unless *c* + 0 at time *t*-1

*vj* = (1,2,3,4), ban *c* + 0 at *t+1*, unless *c* + 0 at *t*-1 (black-and-white)

*vj* = (1,2,3,4,5), ban *c* + 0

*vj* = (0,1,2,3,4), ban *c* + 0

*vj* = (0,1,2,3,4), ban *c* + 0 (black-and-white)

*vj* = (1,2,3,4), ban *c* + 2 at *t*+1 unless *c* + 2 at *t*-1 (animated gif)

*vj* = (1,2,3,4), ban *c* + various at *t*+1 unless *c* + various at *t*-1 (animated gif)

*vj* = (1,2,3,4,5), ban *c* + 0 at *t*+1 unless *c* + 0 at *t*-1

*vj* = (-2,-1,0,1,2), ban *c* + 0

*vj* = (-2,-1,0,1,2), ban *c* + 0 (black-and-white)

*vj* = (0,1,2,3,4), ban *c* + va unless *c* + va

*v* = 5, *vj* = (1,2,3,4), ban *c* + 0

*v* = 5, *vj* = (1,2,3,4), ban *c* + 2

*v* = 5, *vj* = (0,1,2,3), ban *c* + 3

*v* = 6, *vj* = (0,1,2,3), ban *c* + 2

*v* = 5, *vj* = va, ban *c* + va (animated gif)

Filed under: Fractals, Geometry, Mathematics Tagged: animated gif, animated gifs, fractal, fractal geometry, fractals, geometry, hexagon, math, mathematics, maths, pentagon, recreational math, recreational mathematics, recreational maths, squares, vertex of a square, vertices of a square ]]>

1. In terms of “in terms of”, how

oftendo you hear this phantasmagoric phrase in terms of a daily basis?2. Please hierarchialize the following core components of the counter-cultural icon community in terms of their “in-terms-of”-usage

metrics: Will Self, J.G. Ballard, William Burroughs, Alan Moore, Miriam Stimbers, Michael Moorcock, Kathy Acker, Genesis P. Orridge, Alan Ginsberg, Stewart Home, Hubert Selby Jr., Norman Foreman (B.A.). (I.e., if you think Foreman uses “in terms of” most in terms of usage metrics, put him first; if you think Acker uses it second-most, put her second; etc.)3. Engage issues around 1 and 2 again, replacing “in terms of” with “prior to”…

4. Engage issues around 1 and 2

again, replacing “in terms of” with “issues around”……5. Engage issues around 1 and 2

, replacing “in terms of” with “Vote Corbyn”………again

Once you’ve engaged issues around the above issues, email your answers to Evaluator!@NakedKrunch and you should have your doubts laid to rest within 23 working days…

Previously pre-posted on Overlord of the Über-Feral…

• Les Sez

• Don’t Do Dot…

• Terminator!

• Metricizing Michael…

• Terminal Breach

• More Termination…

Filed under: Über-Transgression..., English Usage, Guardianistas, In Terms Of, Transgression... Tagged: 23 working days, Alan Moore, Are U Worthy?, counter-cultural, counter-cultural community, counter-culture, daily basis, dot dot dot, Genesis P-Orridge, Guardianese, Guardianistas, in terms of, issues around, J.G. Ballard, Jeremy Corbyn, Kathy Acker, keyly committed core components of the counter-cultural community, Michael Moorcock, nagged by doubts, Norman Foreman B.A., phantasmagoric phrase, prior to, Stewart Home, The Guardian, transgression, transgressive, twenty-three, Vote Corbyn, Will Self, William Burroughs ]]>

“The substance of God is spherical, in no way resembling man. He is all eye and all ear, but does not breathe; he is the totality of mind and thought, and is eternal.” — Xenophanes’ concept of God in Diogenes Laërtius’ *Lives of Eminent Philosophers* (c. 280-320 AD), Book IX, chapter 2 (translated by R.D. Hicks, 1925).

Filed under: Literature, Philosophy, Post-Weird, Quotations, Theology Tagged: all ear, all eye, ancient Greece, ancient Greek concepts of God, classical Greek, Diogenes Laërtius, eternity, fifth century BC, God, God is spherical, Greek language, Greek philosopher, Greek philosophy, Lives of Eminent Philosophers, Lives of the Philosophers, quotations about God, R.D. Hicks, sixth century BC, spherical God, theology, Trinity Cambridge, Xenophanes ]]>

**distal**, *adj.* *Anat.* Situated away from the centre of the body, or from the point of origin (said of the extremity or distant part of a limb or organ); terminal. Opp. to *proximal*. [← stem of *dist-* (in distant *adj.*) + *-al*, after *dorsal*, *ventral*, etc.] — *Oxford English Dictionary*

When a point jumps inside a triangle, moving halfway towards a randomly chosen vertex each time, a fractal known as the Sierpiński triangle appears:

Point jumping halfway towards random vertex of a triangle

Point jumping inside triangle (black-and-white version)

But when a point moves at random in the same way inside a square, no fractal appears. Instead, the interior of the square gradually fills with a haze of pixels:

Point jumping halfway towards random vertex of a square

Now trying imposing restrictions on the point jumping inside a square. If it can’t jump towards a vertex twice in a row, this fractal appears:

Ban consecutive jumps towards same vertex

Ban consecutive jumps towards same vertex (black-and-white version)

Suppose the vertices are numbered from 1 to 4 and the point can’t jump towards the vertex one lower than the previously chosen vertex. That is, if it jumps towards vertex 3, it can’t jump next towards vertex 2, but it can jump towards vertices 1, 3, or 4 (if the vertex is 1, it’s banned from moving towards vertex 4, i.e. 1-1 = 0 = 4). Now this fractal appears:

Ban jump towards vertex *v*-1

This is the fractal when the point can’t jump towards the vertex two places lower than the one it has just jumped towards:

Ban jump towards vertex *v*-2

But if you can ban, you can also un-ban. Suppose the point jumps towards vertex

Ban jump *v*-2 at *t*+1 unless jump *v*-1 at *t*-1

Here are some more fractals using the ban / un-ban technique:

Ban / un-ban various

Ban jump *v*+0 at *t*+1 unless jump *v*+1 at *t*-1

Ban jump *v*+1 at *t*+1 unless jump *v*+3 at *t*-1

Ban jump *v*+0 at *t*+1 unless jump *v*+2 at *t*-1

Ban jump *v*+2 at *t*+1 unless jump *v*+2 at *t*-1

Ban / un-ban various

You can also impose or lift bans based not on the vertex the point jumps towards, but on the distance the point jumps. For example, take the radius

Ban / un-ban based on distance jumped

Ban jump into segment *s*+0 of 4

Ban jump into segment *s*+1 from center

Ban jump into segment *s*+2

Ban jump into *s*+2 at *t*+1 unless jump into *s*+2 at at *t*-1

Ban jump into *s*+0 from present point

Ban jump into *s*+2 from present point

Ban jump into *s*+3 from present point

Ban jump into *s*+0 at *t*+1 unless jump into *s*+1 at at *t*-1

It’s easy to think of variants on all these themes, but I’ll leave them as an exercise for the interested reader.

Filed under: Fractals, Geometry, Mathematics Tagged: animated gif, animated gifs, chaos game, distal, distality, fractal, fractal geometry, fractals, geometry, math, mathematics, maths, point jumping at random, point moving at random, random point, recreational math, recreational mathematics, recreational maths, Sierpiński triangle, simple fractals, squares, triangles, vertex of a square, vertices of a square ]]>

Filed under: Natural History, Photography Tagged: alpine parrot, kea, Nestor notabilis, New Zealand, New Zealand birds, parrot, parrots, Strigopidae, the South Island, wildlife photography ]]>

• Reds in the Head – *The War of the Worlds*, H.G. Wells (1898)

• Canine the Barbarian – *The Call of the Wild, White Fang, and Other Stories*, Jack London (Penguin American Library 1981)

• Star-Stuff – *The Universe in 100 Key Discoveries*, Giles Sparrow (Quercus 2012)

• An Island of Her Own – *The Phantom Atlas: The Greatest Myths, Lies and Blunders on Maps*, Edward Brooke-Hitching (Simon & Schuster 2016)

Or Read a Review at Random: RaRaR

Filed under: Astronomy, Book Reviews, Literature, Science Tagged: adventure, astronomy, book reviews, cartography, English literature, H.G. Wells, islands, Jack London, legendary places, literature, maps, novels, phantom islands, science fiction, The Call of the Wild, War of the Worlds, White Fang ]]>

Sierpiński triangle from point jumping halfway to randomly chosen vertex

Sierpiński pentagon from point jumping halfway to randomly chosen vertex

But it doesn’t work with a square. Instead, the interior of the square slowly fills with random points:

Square filling with point jumping halfway to randomly chosen vertex

As I showed in Polymorphous Perverticity, you can create fractals from squares and randomly moving points if you ban the point from choosing the same vertex twice in a row, and so on. But there are other ways. You can take the point, move it towards a vertex at random, then swing it around the center of the square through some angle before you mark its position, like this:

Point moves at random, then swings by 90° around center

Point moves at random, then swings by 180° around center

You can also adjust the distance of the point from the center of the square using a formula like

Point moves at random, *dist* = *r* * 0.05 – *dist*

Point moves at random, *dist* = *r* * 0.1 – *dist*

Point moves at random, *dist* = *r* * 0.2 – *dist*

But you can swing the point while applying a vertex-ban, like banning the previously chosen vertex, or the vertex 90° or 180° away. In fact, swinging the points converts one kind of vertex ban into the others.

Point moves at random towards vertex not chosen previously

Point moves at random, then swings by 45°

Point moves at random, then swings by 360°

Point moves at random, then swings by 697.5°

Point moves at random, then swings by 720°

Point moves at random, then swings by 652.5°

Animated angle swing

You can also reverse the swing at every second move, swing the point around a vertex instead of the center or around a point on the circle that encloses the square. Here are some of the fractals you get applying these techniques.

Point moves at random, then swings alternately by 45°, -45°

Point moves at random, then swings alternately by 90°, -90°

Point moves at random, then swings alternately by 135°, -135°

Point moves at random, then swings alternately by 180°, -180°

Point moves at random, then swings alternately by 225°, -225°

Point moves at random, then swings alternately by 315°, -315°

Point moves at random, then swings alternately by 360°, -360°

Animated alternate swing

Point moves at random, then swings around point on circle by 45°

Point moves at random, then swings around point on circle by 67.5°

Point moves at random, then swings around point on circle by 90°

Point moves at random, then swings around point on circle by 112.5°

Point moves at random, then swings around point on circle by 135°

Point moves at random, then swings around point on circle by 180°

Animated circle swing

Filed under: Fractals, Geometry, Mathematics Tagged: animated gif, animated gifs, fractal, fractal geometry, fractals, geometry, math, mathematics, maths, pentagons, random vertex, randomness, recreational math, recreational mathematics, recreational maths, simple fractals, squares, triangles ]]>

“There was no longer anything in the street but shopkeepers and cats.” — Camus, *The Outsider*.

Filed under: Literature, Quotations Tagged: 1942, absurd, absurdity, Albert Camus, Camus, cats, existentialism, French language, French literature, L'étranger, les chats, modern French literature, The Outsider ]]>

Isosceles right triangle

It’s mirror-symmetrical, so it looks the same in a mirror unless you label one of the acute-angled corners in some way, like this:

Right triangle with labelled corner

Right triangle reflected

Reflection is how you find the hourglass fractal. First, divide a right triangle into four smaller right triangles.

Right triangle rep-tiled

Then discard one of the smaller triangles and repeat. If the acute corners of the smaller triangles have different orientations, one of the permutations creates the hourglass fractal, like this:

Hourglass #1

Hourglass #2

Hourglass #3

Hourglass #4

Hourglass #5

Hourglass #6

Hourglass #7

Hourglass #8

Hourglass #9

Hourglass animated

Another permutation of corners creates what I’ve decided to call the crane fractal, like this:

Crane fractal animated

Crane fractal (static)

The crane fractal is something else that I first found playing with the L-triomino:

Crane fractal from L-triomino

Previously pre-posted:

Filed under: Fractals, Geometry, Mathematics, Rep-tiles Tagged: animated gif, animated gifs, crane fractal, fractal, fractal geometry, fractals, fractals from triangles, geometry, hourglass fractal, isosceles right triangles, isosceles triangles, math, mathematics, maths, mirror symmetry, mirror-symmetrical, recreational math, recreational mathematics, recreational maths, right triangles, simple fractals, triangles ]]>